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G4QAOLowEnergyLoss.cc
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27 // -------------------------------------------------------------
28 // GEANT 4 class implementation file
29 //
30 // History: New Implementation
31 //
32 // ---------- G4QAOLowEnergyLoss physics process -------
33 // by Stephane Chauvie, 5 May 2000
34 // Modified:
35 //
36 // 24/05/2000 MGP Modified to remove compilation warnings on Linux and DEC
37 // Introduced sizes of L0, L1, L2 arrays
38 // 23/05/2000 MGP Made compliant to design
39 // 02/08/2000 V.Ivanchenko Clean up according new design
40 // 16/09/2000 S. Chauvie Oscillator for all materials
41 // 03/10/2000 V.Ivanchenko CodeWizard clean up
42 // 05/11/2000 V.Ivanchenko "Aluminum" - correct name, end of cycle
43 // over shells, and two bugs from previous edition
44 // 10/05/2001 V.Ivanchenko Clean up againist Linux compilation with -Wall
45 // 13/05/2001 S. Chauvie corrected bugs
46 // 01/06/2001 V.Ivanchenko replace names by Z, change the validity range
47 // from 50 keV to 5 KeV and change sign of the
48 // Barkas term
49 // 4/06/2001 S. Chauvie Corrected small bugs
50 //
51 // ************************************************************
52 // It is the Quantal Harmonic Oscillator Model for energy loss
53 // of slow antiproton
54 // ************************************************************
55 // --------------------------------------------------------------
56 
57 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
58 
59 #include "G4QAOLowEnergyLoss.hh"
60 #include "G4PhysicalConstants.hh"
61 #include "G4SystemOfUnits.hh"
62 #include "G4DynamicParticle.hh"
63 #include "G4Material.hh"
64 #include "G4ParticleDefinition.hh"
65 #include "G4AntiProton.hh"
66 #include "G4Exp.hh"
67 
68 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
69 
70 G4QAOLowEnergyLoss::G4QAOLowEnergyLoss(const G4String& name)
71  : G4VLowEnergyModel(name)
72 {
73  numberOfMaterials = 6;
74  sizeL0 = 67;
75  sizeL1 = 22;
76  sizeL2 = 14;
77 }
78 
79 
80 G4QAOLowEnergyLoss::~G4QAOLowEnergyLoss()
81 {;}
82 
83 
84 G4double G4QAOLowEnergyLoss::HighEnergyLimit(const G4ParticleDefinition* ,
85  const G4Material* ) const
86 {
87  return 2.0*MeV ;
88 }
89 
90 
91 G4double G4QAOLowEnergyLoss::LowEnergyLimit(const G4ParticleDefinition* ,
92  const G4Material* ) const
93 {
94  // return 50.0*keV ;
95  return 5.0*keV ;
96 }
97 
98 
99 G4double G4QAOLowEnergyLoss::HighEnergyLimit(const G4ParticleDefinition* ) const
100 {
101  return 2.0*MeV ;
102 }
103 
104 G4double G4QAOLowEnergyLoss::LowEnergyLimit(const G4ParticleDefinition* ) const
105 {
106  // return 50.0*keV ;
107  return 5.0*keV ;
108 }
109 
110 
111 G4bool G4QAOLowEnergyLoss::IsInCharge(const G4DynamicParticle* particle,
112  const G4Material* material) const
113 {
114  G4bool isInCharge = false;
115 
116  G4bool hasMaterial = false;
117 
118  if (material->GetNumberOfElements() == 1) hasMaterial = true;
119 
120  if ((particle->GetDefinition()) == (G4AntiProton::AntiProtonDefinition())
121  && hasMaterial) isInCharge = true;
122 
123  return isInCharge;
124 
125 }
126 
127 G4bool G4QAOLowEnergyLoss::IsInCharge(const G4ParticleDefinition* aParticle,
128  const G4Material* material) const
129 {
130 
131  G4bool isInCharge = false;
132 
133  G4bool hasMaterial = false;
134 
135  if (material->GetNumberOfElements() == 1) hasMaterial = true;
136 
137 
138  if (aParticle == (G4AntiProton::AntiProtonDefinition())
139  && hasMaterial) isInCharge = true;
140 
141  return isInCharge;
142 
143 }
144 
145 
146 G4double G4QAOLowEnergyLoss::TheValue(const G4DynamicParticle* particle,
147  const G4Material* material)
148 {
149  G4double zParticle = (G4int)(particle->GetCharge())/eplus;
150 
151  G4double energy = particle->GetKineticEnergy() ;
152  G4double eloss = EnergyLoss(material,energy,zParticle) ;
153 
154  return eloss ;
155 }
156 
157 
158 G4double G4QAOLowEnergyLoss::TheValue(const G4ParticleDefinition* aParticle,
159  const G4Material* material,
160  G4double kineticEnergy)
161 {
162  G4double zParticle = (aParticle->GetPDGCharge())/eplus;
163 
164  G4double eloss = EnergyLoss(material,kineticEnergy,zParticle) ;
165 
166  return eloss ;
167 }
168 
169 
170 
171 G4double G4QAOLowEnergyLoss::EnergyLoss(const G4Material* material,
172  G4double kineticEnergy,
173  G4double zParticle) const
174 {
175  G4int nbOfShell = GetNumberOfShell(material);
176  if(nbOfShell < 1) nbOfShell = 1;
177 
178  //G4int iz = (G4int)(material->GetZ());
179  //if(iz < 1) iz = 1;
180  //else if(iz > 100) iz = 100;
181  //G4int nbOfShell = fNumberOfShells[iz];
182 
183  /*
184  if(material->GetName()=="Graphite"){
185  G4cout << " E(MeV)= " << kineticEnergy/MeV << " n= "
186  << nbOfShell
187  << " for " << material->GetZ() << G4endl;
188  }
189  */
190  G4double dedx=0;
191 
192  G4double v = c_light * std::sqrt( 2.0 * kineticEnergy / proton_mass_c2 );
193  G4double coeff = twopi * proton_mass_c2 *
194  (material-> GetTotNbOfElectPerVolume()) /
195  electron_mass_c2 ;
196  G4double fBetheVelocity = fine_structure_const * c_light / v;
197  coeff *= fine_structure_const * fine_structure_const * hbarc_squared /
198  kineticEnergy ;
199 
200  //G4double beta = std::sqrt( 2.0 * kineticEnergy / proton_mass_c2 );
201  //G4double fBetheVelocity = std::sqrt( 2.0 * 25.0 * keV / proton_mass_c2 )/beta;
202  //G4double coeff= twopi_mc2_rcl2*(material->GetElectronDensity())/(beta*beta);
203 
204 
205  G4double l0Term = 0, l1Term = 0, l2Term = 0;
206 
207  for (G4int nos = 0 ; nos < nbOfShell ; nos++){
208 
209  G4double l0 = 0, l1 = 0, l2 = 0;
210  G4double NormalizedEnergy = ( 2.0 * electron_mass_c2 * v * v ) /
211  ( c_squared * GetShellEnergy(material,nos) );
212  //G4double NormalizedEnergy = ( 2.0 * electron_mass_c2 * beta * beta ) /
213  // GetShellEnergy(material,nos);
214  G4double shStrength = GetShellStrength(material,nos);
215 
216  l0 = GetL0(NormalizedEnergy);
217  l0Term += shStrength * l0;
218 
219  l1 = GetL1(NormalizedEnergy);
220  l1Term += shStrength * l1;
221 
222  l2 = GetL2(NormalizedEnergy);
223  l2Term += shStrength * l2;
224 
225  /*
226  if(material->GetName()=="Graphite"){
227  G4cout << nos << ". "
228  << " E(MeV)= " << kineticEnergy/MeV
229  << " normE= " << NormalizedEnergy
230  << " sh en= " << GetShellEnergy(material,nos)
231  << " str= " << shStrength
232  << " v0/v= " << fBetheVelocity
233  << " l0= " << l0Term
234  << " l1= " << l1Term
235  << " l2= " << l2Term
236  << G4endl;
237  }
238  */
239  }
240 
241  dedx = coeff * zParticle * zParticle * (l0Term
242  + zParticle * fBetheVelocity * l1Term
243  + zParticle * zParticle * fBetheVelocity * fBetheVelocity * l2Term);
244 
245  // G4cout << " E(MeV)= " << kineticEnergy/MeV
246  // << " dedx(Mev/mm)= " << dedx*mm/MeV << G4endl;
247 
248  return dedx ;
249 
250 }
251 
252 
253 G4int G4QAOLowEnergyLoss::GetNumberOfShell(const G4Material* material) const
254 {
255  // Set return value from table
256  G4int Z = (G4int)(material->GetZ());
257  G4int nShell = 0;
258 
259  // Set return value if in material available from Aahrus
260  for(G4int i=0; i<numberOfMaterials; i++) {
261 
262  if(materialAvailable[i] == Z){
263  nShell = nbofShellForMaterial[i];
264  break;
265  }
266  else nShell = fNumberOfShells[Z];
267  }
268 
269  return nShell;
270 }
271 
272 
273 
274 G4double G4QAOLowEnergyLoss::GetShellEnergy(const G4Material* material,
275  G4int nbOfTheShell) const
276 {
277  //
278  G4double shellEnergy = alShellEnergy[0];
279 
280  if(material->GetZ() == 13) shellEnergy = alShellEnergy[nbOfTheShell];
281  else if(material->GetZ() == 14)shellEnergy = siShellEnergy[nbOfTheShell];
282  else if(material->GetZ() == 29)shellEnergy = cuShellEnergy[nbOfTheShell];
283  else if(material->GetZ() == 73)shellEnergy = taShellEnergy[nbOfTheShell];
284  else if(material->GetZ() == 79)shellEnergy = auShellEnergy[nbOfTheShell];
285  else if(material->GetZ() == 78)shellEnergy = ptShellEnergy[nbOfTheShell];
286  else if (material->GetNumberOfElements() == 1)
287  shellEnergy = GetOscillatorEnergy(material, nbOfTheShell);
288  else G4cout << "WARNING - G4QAOLowEnergyLoss::GetShellEnergy - "
289  << "The model is not available for "
290  << material->GetName()
291  << G4endl;
292 
293  return shellEnergy;
294 }
295 
296 
297 G4double G4QAOLowEnergyLoss::GetOscillatorEnergy(const G4Material* material,
298  G4int nbOfTheShell) const
299 {
300 
301  const G4Element* element = material->GetElement(0);
302 
303  G4int Z = (G4int)(element->GetZ());
304 
305 G4double squaredPlasmonEnergy = 28.816 * 28.816 * 1e-6
306  * material->GetDensity()/g/cm3
307  * (Z/element->GetN()) ;
308 //G4double squaredPlasmonEnergy = 28.16 * 28.16 * 1e-6
309 // * (material->GetDensity()) * (cm3/g)
310 // * Z / (element->GetN()) ;
311 
312  G4double plasmonTerm = 0.66667 * GetOccupationNumber(Z,nbOfTheShell)
313  * squaredPlasmonEnergy / (Z*Z) ;
314 
315  G4double ionTerm = G4Exp(0.5) * (element->GetAtomicShell(nbOfTheShell)) ;
316 
317  ionTerm = ionTerm*ionTerm ;
318 
319  G4double oscShellEnergy = std::sqrt( ionTerm + plasmonTerm );
320 
321 /* if(material->GetName()=="Graphite"){
322  G4cout << "\t" << Z
323  << "\t" << nbOfTheShell
324  << "\t" << squaredPlasmonEnergy
325  << "\t" << plasmonTerm
326  << "\t" << ionTerm
327  << "\t" << GetOccupationNumber(Z,nbOfTheShell)
328  << "\t" << element->GetAtomicShell(nbOfTheShell)
329  << "\t" << oscShellEnergy << G4endl;}
330 */
331  return oscShellEnergy;
332 }
333 
334 G4double G4QAOLowEnergyLoss::GetShellStrength(const G4Material* material,
335  G4int nbOfTheShell) const
336 {
337  G4double shellStrength = alShellStrength[0];
338 
339  if(material->GetZ() == 13) shellStrength = alShellStrength[nbOfTheShell];
340  else if(material->GetZ() == 14)shellStrength =siShellStrength[nbOfTheShell];
341  else if(material->GetZ() == 29)shellStrength =cuShellStrength[nbOfTheShell];
342  else if(material->GetZ() == 73)shellStrength =taShellStrength[nbOfTheShell];
343  else if(material->GetZ() == 79)shellStrength =auShellStrength[nbOfTheShell];
344  else if(material->GetZ() == 78)shellStrength =ptShellStrength[nbOfTheShell];
345  else if (material->GetNumberOfElements() == 1){
346  G4int Z = (G4int)(material->GetZ());
347  shellStrength = GetOccupationNumber(Z,nbOfTheShell) / Z ;}
348  else G4cout << "WARNING - G4QAOLowEnergyLoss::GetShellEnergy - "
349  << "The model is not available for "
350  << material->GetName()
351  << G4endl;
352 
353  return shellStrength;
354 }
355 
356 G4double G4QAOLowEnergyLoss::GetOccupationNumber(G4int Z, G4int ShellNb) const
357 {
358 
359  G4int indice = ShellNb ;
360  for (G4int z = 1 ; z < Z ; z++) {indice += fNumberOfShells[z];}
361 
362  return nbOfElectronPerSubShell[indice+1];
363 }
364 
365 
366 G4double G4QAOLowEnergyLoss::GetL0(G4double normEnergy) const
367 {
368  G4int n;
369 
370  for(n = 0; n < sizeL0; n++) {
371  if( normEnergy < L0[n][0] ) break;
372  }
373  if(0 == n) n = 1 ;
374  if(n >= sizeL0) n = sizeL0 - 1 ;
375 
376  G4double l0 = L0[n][1];
377  G4double l0p = L0[n-1][1];
378  G4double bethe = l0p + (l0 - l0p) * ( normEnergy - L0[n-1][0]) /
379  (L0[n][0] - L0[n-1][0]);
380  return bethe ;
381 
382 }
383 
384 G4double G4QAOLowEnergyLoss::GetL1(G4double normEnergy) const
385 {
386  G4int n;
387 
388  for(n = 0; n < sizeL1; n++) {
389  if( normEnergy < L1[n][0] ) break;
390  }
391  if(0 == n) n = 1 ;
392  if(n >= sizeL1) n = sizeL1 - 1 ;
393 
394  G4double l1 = L1[n][1];
395  G4double l1p = L1[n-1][1];
396  G4double barkas= l1p + (l1 - l1p) * ( normEnergy - L1[n-1][0]) /
397  (L1[n][0] - L1[n-1][0]);
398 
399  return barkas;
400 
401 }
402 
403 
404 G4double G4QAOLowEnergyLoss::GetL2(G4double normEnergy) const
405 {
406  G4int n;
407  for(n = 0; n < sizeL2; n++) {
408  if( normEnergy < L2[n][0] ) break;
409  }
410  if(0 == n) n = 1 ;
411  if(n >= sizeL2) n = sizeL2 - 1 ;
412 
413  G4double l2 = L2[n][1];
414  G4double l2p = L2[n-1][1];
415  G4double bloch = l2p + (l2 - l2p) * ( normEnergy - L2[n-1][0]) /
416  (L2[n][0] - L2[n-1][0]);
417 
418  return bloch;
419 }
420 
421 
422 const G4int G4QAOLowEnergyLoss::materialAvailable[6] = {13,14,29,73,79,78};
423  /*
424  "Aluminum",
425  "Silicon",
426  "Copper",
427  "Tantalum",
428  "Gold",
429  "Platinum"};
430  */
431 const G4int G4QAOLowEnergyLoss::nbofShellForMaterial[6] = {3,3,4,6,6,6 };
432 
433 const G4double G4QAOLowEnergyLoss::alShellEnergy[3] ={ 2795e-6, 202e-6, 16.9e-6};
434 const G4double G4QAOLowEnergyLoss::alShellStrength[3]={ 0.1349, 0.6387, 0.2264};
435 const G4double G4QAOLowEnergyLoss::siShellEnergy[3] ={ 3179e-6, 249e-6, 20.3e-6 };
436 const G4double G4QAOLowEnergyLoss::siShellStrength[3]={ 0.1222, 0.5972, 0.2806};
437 const G4double G4QAOLowEnergyLoss::cuShellEnergy[4] ={ 16931e-6, 1930e-6, 199e-6, 39.6e-6};
438 const G4double G4QAOLowEnergyLoss::cuShellStrength[4]={ 0.0505, 0.2561, 0.4913, 0.2021};
439 const G4double G4QAOLowEnergyLoss::taShellEnergy[6] ={ 88926e-6, 18012e-6, 3210e-6, 575e-6, 108.7e-6, 30.8e-6};
440 const G4double G4QAOLowEnergyLoss::taShellStrength[6]={ 0.0126, 0.0896, 0.2599, 0.3413, 0.2057, 0.0908};
441 const G4double G4QAOLowEnergyLoss::auShellEnergy[6]={ 96235e-6, 25918e-6, 4116e-6, 599e-6, 87.3e-6, 36.9e-6};
442 const G4double G4QAOLowEnergyLoss::auShellStrength[6]={ 0.0139, 0.0803, 0.2473, 0.423, 0.1124, 0.1231};
443 const G4double G4QAOLowEnergyLoss::ptShellEnergy[6]={ 95017e-6, 25590e-6, 4063e-6, 576e-6, 81.9e-6, 31.4e-6};
444 const G4double G4QAOLowEnergyLoss::ptShellStrength[6]={ 0.0129, 0.0745, 0.2295, 0.4627, 0.1324, 0.0879};
445 
446 
447 const G4double G4QAOLowEnergyLoss::L0[67][2] =
448 {
449  {0.00, 0.000001},
450  {0.10, 0.000001},
451  {0.12, 0.00001},
452  {0.14, 0.00005},
453  {0.16, 0.00014},
454  {0.18, 0.00030},
455  {0.20, 0.00057},
456  {0.25, 0.00189},
457  {0.30, 0.00429},
458  {0.35, 0.00784},
459  {0.40, 0.01248},
460  {0.45, 0.01811},
461  {0.50, 0.02462},
462  {0.60, 0.03980},
463  {0.70, 0.05731},
464  {0.80, 0.07662},
465  {0.90, 0.09733},
466  {1.00, 0.11916},
467  {1.20, 0.16532},
468  {1.40, 0.21376},
469  {1.60, 0.26362},
470  {1.80, 0.31428},
471  {2.00, 0.36532},
472  {2.50, 0.49272},
473  {3.00, 0.61765},
474  {3.50, 0.73863},
475  {4.00, 0.85496},
476  {4.50, 0.96634},
477  {5.00, 1.07272},
478  {6.00, 1.27086},
479  {7.00, 1.45075},
480  {8.00, 1.61412},
481  {9.00, 1.76277},
482  {10.00, 1.89836},
483  {12.00, 2.13625},
484  {14.00, 2.33787},
485  {16.00, 2.51093},
486  {18.00, 2.66134},
487  {20.00, 2.79358},
488  {25.00, 3.06539},
489  {30.00, 3.27902},
490  {35.00, 3.45430},
491  {40.00, 3.60281},
492  {45.00, 3.73167},
493  {50.00, 3.84555},
494  {60.00, 4.04011},
495  {70.00, 4.20264},
496  {80.00, 4.34229},
497  {90.00, 4.46474},
498  {100.00, 4.57378},
499  {120.00, 4.76155},
500  {140.00, 4.91953},
501  {160.00, 5.05590},
502  {180.00, 5.17588},
503  {200.00, 5.28299},
504  {250.00, 5.50925},
505  {300.00, 5.69364},
506  {350.00, 5.84926},
507  {400.00, 5.98388},
508  {450.00, 6.10252},
509  {500.00, 6.20856},
510  {600.00, 6.39189},
511  {700.00, 6.54677},
512  {800.00, 6.68084},
513  {900.00, 6.79905},
514  {1000.00, 6.90474}
515 };
516 
517 const G4double G4QAOLowEnergyLoss::L1[22][2] =
518 {
519  {0.00, -0.000001},
520  {0.10, -0.00001},
521  {0.20, -0.00049},
522  {0.30, -0.00084},
523  {0.40, 0.00085},
524  {0.50, 0.00519},
525  {0.60, 0.01198},
526  {0.70, 0.02074},
527  {0.80, 0.03133},
528  {0.90, 0.04369},
529  {1.00, 0.06035},
530  {2.00, 0.24023},
531  {3.00, 0.44284},
532  {4.00, 0.62012},
533  {5.00, 0.77031},
534  {6.00, 0.90390},
535  {7.00, 1.02705},
536  {8.00, 1.10867},
537  {9.00, 1.17546},
538  {10.00, 1.21599},
539  {15.00, 1.24349},
540  {20.00, 1.16752}
541 };
542 
543 const G4double G4QAOLowEnergyLoss::L2[14][2] =
544 {
545  {0.00, 0.000001},
546  {0.10, 0.00001},
547  {0.20, 0.00000},
548  {0.40, -0.00120},
549  {0.60, -0.00036},
550  {0.80, 0.00372},
551  {1.00, 0.01298},
552  {2.00, 0.08296},
553  {4.00, 0.21953},
554  {6.00, 0.23903},
555  {8.00, 0.20893},
556  {10.00, 0.10879},
557  {20.00, -0.88409},
558  {40.00, -1.13902}
559 };
560 
561 const G4int G4QAOLowEnergyLoss::nbOfElectronPerSubShell[1540] =
562 {
563  0, // consistency with G4AtomicShells
564  1,//------ H
565  2,//------ He
566  2, 1,//------ Li
567  2, 2,//------ Be
568  2, 2, 1,//------ B
569  2, 2, 2,//------ C
570  2, 2, 2, 1,//------ N
571  2, 2, 2, 2,//------ O
572  2, 2, 5,//------ F
573  2, 2, 2, 4,//------ Ne
574  2, 2, 2, 4, 1,//------ Na
575  2, 2, 2, 4, 2,//------ Mg
576  2, 2, 2, 4, 2, 1,//------ Al
577  2, 2, 2, 4, 2, 2,//------ Si
578  2, 2, 2, 4, 2, 3,//------ P
579  2, 2, 2, 4, 2, 4,//------
580  2, 2, 2, 4, 2, 5,//------
581  2, 2, 2, 4, 2, 2, 4,//------
582  2, 2, 2, 4, 2, 2, 4, 1,//------
583  2, 2, 2, 4, 2, 2, 4, 2,//------
584  2, 2, 2, 4, 2, 2, 4, 1, 2,//------
585  2, 2, 2, 4, 2, 2, 4, 2, 2,//------
586  2, 2, 2, 4, 2, 2, 4, 3, 2,//------
587  2, 2, 2, 4, 2, 2, 4, 4, 2,//------
588  2, 2, 2, 4, 2, 2, 4, 5, 2,//------
589  2, 2, 2, 4, 2, 2, 4, 6, 2,//------
590  2, 2, 2, 4, 2, 2, 4, 7, 2,//------
591  2, 2, 2, 4, 2, 2, 4, 4, 4, 2,//------
592  2, 2, 2, 4, 2, 2, 4, 4, 5, 2,//------
593  2, 2, 2, 4, 2, 2, 4, 4, 6, 2,//------
594  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 1,//------
595  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2,//------
596  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 3,//------
597  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 4,//------
598  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 5,//------
599  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4,//------
600  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
601  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
602  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
603  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 2, 2,//------
604  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 3, 2,//------
605  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 2,//------
606  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 5, 2,//------
607  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 6, 2,//------
608  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 7, 2,//------
609  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 4, 2,//------
610  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 5, 2,//------
611  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2,//------
612  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 1,//------
613  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2,//------
614  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 3,//------
615  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 4,//------
616  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 5,//------
617  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4,//------
618  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
619  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
620  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
621  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 2, 4, 2,//------
622  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 3, 2, 2, 4, 2,//------
623  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 4, 2, 2, 4, 2,//------
624  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 5, 2, 2, 4, 2,//------
625  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 2, 2, 4, 2,//------
626  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 7, 2, 2, 4, 2,//------
627  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 7, 2, 2, 4, 1, 2,//------
628  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 9, 2, 2, 4, 2,//------
629  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 10, 2, 2, 4, 2,//------
630  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 11, 2, 2, 4, 2,//------
631  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 12, 2, 2, 4, 2,//------
632  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 13, 2, 2, 4, 2,//------
633  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 2,//------
634  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 1, 2,//------
635  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 2, 2,//------
636  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 3, 2,//------
637  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 2,//------
638  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 5, 2,//------
639  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 6, 2,//------
640  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 7, 2,//------
641  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 9, 1,//------
642  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 1,//------
643  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2,//------
644  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 1,//------
645  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2,//------
646  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 3,//------
647  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 4,//------
648  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 3,//------
649  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4,//------
650  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
651  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
652  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
653  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 2, 2,//------
654  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 2, 4, 1, 2,//------
655  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 3, 2, 2, 4, 1, 2,//------
656  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 4, 2, 2, 4, 1, 2,//------
657  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 6, 2, 2, 4, 2,//------
658  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 7, 2, 2, 4, 2,//------
659  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 7, 2, 2, 4, 1, 2,//------
660  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 8, 2, 2, 4, 1, 2,//------
661  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 10, 2, 2, 4, 2,//------
662  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 11, 2, 2, 4, 2,//------
663  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 12, 2, 2, 4, 2 //-----
664 };
665 
666 const G4int G4QAOLowEnergyLoss::fNumberOfShells[101] =
667 {
668  0 , // nonexisting zero element
669 
670  1 , 1 , 2 , 2 , 3 , 3 , 4 , 4 , 3 , 4 , // 1 - 10
671 
672  5 , 5 , 6 , 6 , 6 , 6 , 6 , 7 , 8 , 8 , // 11 - 20
673 
674  9 , 9 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 10 , // 21 - 30
675 
676 11 , 11 , 11 , 11 , 11 , 12 , 13 , 13 , 14 , 14 , // 31 - 40
677 
678 14 , 14 , 14 , 14 , 14 , 15 , 15 , 15 , 16 , 16 , // 41 - 50
679 
680 // ----------------------------------------------------------
681 
682 16 , 16 , 16 , 17 , 18 , 18 , 19 , 19 , 19 , 19 , // 51 - 60
683 
684 19 , 19 , 19 , 20 , 19 , 19 , 19 , 19 , 19 , 20 , // 61 - 70
685 
686 21 , 21 , 21 , 21 , 21 , 21 , 21 , 21 , 22 , 22 , // 71 - 80
687 
688 23 , 23 , 23 , 23 , 24 , 24 , 25 , 25 , 26 , 26 , // 81 - 90
689 
690 27 , 27 , 27 , 26 , 26 , 27 , 27 , 26 , 26 , 26 // 91 - 100
691 
692 };